On Rockafellar’s theorem using proximal point algorithm involving -maximal monotonicity framework

On the basis of the general framework of H-maximal monotonicity (also referred to as H-monotonicity in the literature), a generalization to Rockafellar’s theorem in the context of solving a general inclusion problem involving a set-valued maximal monotone operator using the proximal point algorithm in a Hilbert space setting is explored. As a matter of fact, this class of inclusion problems reduces to a class of variational inequalities as well as to a class of complementarity problems. This proximal point algorithm turns out to be of interest in the sense that it plays a significant role in certain computational methods of multipliers in nonlinear programming. The notion of H-maximal monotonicity generalizes the general theory of set-valued maximal monotone mappings to a new level. Furthermore, some results on general firm nonexpansiveness and resolvent mapping corresponding to H-monotonicity are also given.     

On a finite difference scheme for Burgers’ equation

In this paper we study properties of numerical solutions of Burger’s equation. Burgers’ equation is reduced to the heat equation on which we apply the Douglas finite difference scheme. The method is shown to be unconditionally stable, fourth order accurate in space and second order accurate in time. Two test problems are used to validate the algorithm. Numerical solutions for various values of viscosity are calculated and it is concluded that the proposed method performs well.     

Templated growth of hybrid structures at the peptide-peptide interface

This study describes the use of peptide vesicular platforms for the templated growth of fibrillar structures to craft hybrids that retain the gross morphological features of two discreet self-assembled peptides. A synthetic triskelion peptide, which results in the rapid emergence of self-assembled spherical structures, was employed as a template. Addition of either one of two different peptides, both of which form long filamentous structures when co-incubated with the triskelion solution, affords hybrids that retain the gross morphology of both the spherical and filamentous structures. It is surmised that this process is aided by hydrogen bonding and the interdigitation of aromatic residues, which leads to the growth of hybrid structures. We believe that observations concerning the surface-assisted growth of peptide fibrils and tubular structures from vesicular platforms may have ramifications for the design and development of peptide-based hybrid materials with controlled hierarchical structures.     

Determination of amoxapine and nortriptyline in blood plasma and serum by salt-assisted liquid-liquid microextraction and high-performance liquid chromatography

A new, selective and sensitive method has been developed for the determination of tricyclic antidepressant drugs, amoxapine and nortriptyline, in human blood plasma and serum, involving their reaction with allyl isothiocyanate and extraction of thiourea derivatives with water-miscible organic solvent acetonitrile. The phase separation was effected by addition of ammonium sulphate, a process called salt-assisted liquid-liquid microextraction. The extract was analyzed by HPLC with UV detection at 254?nm. The method has been optimized for derivatization reaction time and temperature, solvent for extraction, and salt for solvent phase separation. Under the optimal conditions, a linear calibration graph was obtained between the amount of drug and the peak area of thiourea derivatives in the range of 0.002-20?mg/L drugs. The correlation coefficient and limit of detection values for amoxapine and nortriptyline in serum/plasma samples were in the range of 0.9953-0.9999 and 0.46-0.58?μg/L, respectively. The recovery in spiking experiments ranged, respectively, 75-88% (RSD 3.4-7.2%) and 79-97% (RSD 3.7-7.9%) for the two drugs.     

Inter-conversion of Tb3+ and Tb4+ states and its fluorescence properties in MO–Al2O3: Tb (M = Mg,Ca, Sr,Ba) phosphor materials

Terbium ion doped MO–Al₂O₃ (M = Mg, Ca, Sr and Ba) series phosphors have been synthesized through combustion technique and their luminescence properties have been studied and compared. Terbium ion in different phosphors has shown different fluorescence properties due to the presence of different ratios of Tb³⁺ and Tb⁴⁺ states in different samples. The UV/Visible absorption and XPS techniques have been used to probe the existence of Tb³⁺ and Tb⁴⁺ states. The host sensitive 4f–5d and the charge transfer transitions enabled the use of terbium ion as an indicator of the structure.     

Synthesis, spectral and biological studies of nitrogen–sulphur donor macrocyclic ligands and their transition metals complexes

Mn(II), Co(II), Ni(II) and Cu(II) complexes have been synthesized with 22 and 24 membered tetramide macrocyclic ligands viz; 1,9,12,20-tetraaza-2,8,13,19-tetraone-5,16-dithiacyclodocosane [L¹] and 1,9,13,21-tetraaza-2,8,14,20-tetraone-5,17-dithiacyclotetracosane [L²] and characterized by elemental analysis, molar conductance, magnetic susceptibility measurements, mass, IR, electronic EPR spectral studies and electrochemical properties. The molar conductance of all the complexes in DMSO solution is corresponding to 1:2 electrolyte. Thus these complexes may be formulated as [M(L′)]Cl₂ [where M = Mn(II), Co(II), Ni(II) and Cu(II) L′ = L¹ and L²]. On the basis of spectral studies a distorted octahedral geometry has been assigned for all the complexes. The ligands and their complexes were also screened in vitro against two pathogenic fungi (F. moniliformae and R. solani) to assess their growth inhibiting potential.     

Iodine trichloride as an analytical reagent for determination of some organic compounds

Procedures are described for the determination of organic compounds with iodine trichloride under Andrews's titration conditions. Samples are directly titrated with iodine trichloride or first reacted with an excess of iodine monochloride, with subsequent titration of the iodine formed. The direct titration is done initially in feebly acid medium, then the acidity is raised (biotin, methionine, cystine and thiomersal). Pre-oxidation with iodine monochloride is used if the organic compound reacts slowly [tryptophan and arsenic(III) compounds] or is determined in bicarbonate medium (hydroxylamine and thiosemicarbazide). The ferrocyanide formed by the reduction of ferricyanide (by thiourea and allylthiourea) can also be titrated. Arsenic(V) compounds are determined after reduction to arsenic(III), and iodine in organic compounds is converted into iodide by alkaline fusion into iodide and the iodide titrated.     

Alkalimetric determination of mercaptans through trithiocarbonic acid formation

A simple and rapid alkalimetric method for the determination of mercaptans through trithiocarbonic acid formation is described. The mercaptans are titrated in tert.-butanol in the presence of carbon disulphide with standard aqueous sodium hydroxide, with phenolphthalein as indicator. The -SH group is smoothly, rapidly and quantitatively transformed into the group under the specified conditions. The method has been extended to the analysis of mercaptan-carboxylic acid and mercaptan-trithiocarbonate mixtures.     

Amperometric determination of organic isothiocyanates

An amperometric titration method is described for the determination of 1-5 mg of organic isothiocyanates, based on their quantitative reaction with n-butylamine in dimethylfonnamide to form N,N-disubstituted thioureas which are then titrated amperometrically in aqueous ammonia-ammonium nitrate buffer with silver nitrate (dropping mercury electrode at -0.56V). The end-point corresponds to a silver:thiourea ratio of 2:1, with precipitation of silver sulphide. The method is simple, accurate, widely applicable, and gives reproducible results.     

Separation and gravimetric determination of cerium and lanthanum with N-m-tolyl-m-nitrobenzohydroxamic acid

Cerium and lanthanum were determined gravimetrically by selective precipitation with N-m-tolyl-m-nitrobenzohydroxamic acid and separated from several metal ions such as Ag(+), Be(2+) , Pb(2+) , Mn(2+) , Cu(2+), Zn(2+) , Cd(2+) , Hg(2+) , Pd(2+) , Ga(3+) A1(3+) , Bi(3+) , Sb(3+), Sn(4+), Ce(3+) , Pr(3+) , Nd(3+) , Ti(4+), Zr(4+), Th(4+), V(5+) , Mo(6+) and U(6+) . The precipitates were weighted directly after drying at 110 degrees . The analytical results indicated the composition of the complexes to be (C(14)H(11)N(2)O(4))(n)M.